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Implementation of Real Root Isolation Algorithms in Mathematica

Summary: Implementation of Real Root Isolation Algorithms
in Mathematica
Alkiviadis G. Akritas,
University of Kansas, Lawrence;
Alexei V. Bocharov,
Wolfram Research Inc. and Russian Academy of Science;
Adam W. StrzeboŽnski,
Wolfram Research Inc. and Jagiellonian University, KrakŽow
current e-mail address: akritas@uth.gr
In this paper we compare two real root isolation methods using Descartes' Rule
of Signs: the Interval Bisection method, and the Continued Fractions method.
We present some time-saving improvements to both methods. Comparing
computation times we conclude that the Continued Fractions method works
much faster save for the case of very many very large roots.
1 Introduction.
Isolation of real roots of univariate polynomials is the time-critical part of
any algorithm for complex root isolation. Therefore the efficiency of the real
root isolation is essential for developing efficient, guaranteed and precise root-
finding strategies.


Source: Akritas, Alkiviadis G. - Department of Computer and Communication Engineering, University of Thessaly


Collections: Computer Technologies and Information Sciences